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Phenomena in Nonlinear Dynamical Systems: Theory and Application

A special issue of Applied Sciences (ISSN 2076-3417). This special issue belongs to the section "Mechanical Engineering".

Deadline for manuscript submissions: closed (30 April 2025) | Viewed by 2912

Special Issue Editor


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Guest Editor
Faculty of Technical Sciences, University of Novi Sad, Novi Sad, Serbia
Interests: nonlinear vibrations; rotor dynamics; mechanisms with variable mass

Special Issue Information

Dear Colleagues,

Although research in the field of dynamics and oscillations dates back to ancient times, some problems still remain unsolved;  these issues primarily concern non-linearities in systems or processes. The aim of this Special Issue is to publish the results of research on the influence of both physical and geometric nonlinearities on system dynamics. Hence, this issue focuses on research in the dynamics and vibrations of nonlinear mechanical systems and processes. The following topics are of interest:

  • Mathematical modelling of nonlinear dynamical and vibration systems and processes;
  • New analytical and numerical solving procedures for strong nonlinear oscillators;
  • Nonlinear phenomena in dynamic systems;
  • Bifurcation and deterministic chaos;
  • Control in nonlinear oscillators;
  • Analogies between nonlinear mechanical and other systems;
  • Application of nonlinear oscillators in applied sciences and engineering.

The Special Issue on “Phenomena in Nonlinear Dynamical Systems: Theory and Application” welcomes not only submissions on the aforementioned topics but also on all recent research covered by the topic in the title. The call is open to a broad thematic range of papers covering recent applications of dynamics, vibration and control theory.

Prof. Dr. Lívija Cveticanin
Guest Editor

Manuscript Submission Information

Manuscripts should be submitted online at www.mdpi.com by registering and logging in to this website. Once you are registered, click here to go to the submission form. Manuscripts can be submitted until the deadline. All submissions that pass pre-check are peer-reviewed. Accepted papers will be published continuously in the journal (as soon as accepted) and will be listed together on the special issue website. Research articles, review articles as well as short communications are invited. For planned papers, a title and short abstract (about 100 words) can be sent to the Editorial Office for announcement on this website.

Submitted manuscripts should not have been published previously, nor be under consideration for publication elsewhere (except conference proceedings papers). All manuscripts are thoroughly refereed through a single-blind peer-review process. A guide for authors and other relevant information for submission of manuscripts is available on the Instructions for Authors page. Applied Sciences is an international peer-reviewed open access semimonthly journal published by MDPI.

Please visit the Instructions for Authors page before submitting a manuscript. The Article Processing Charge (APC) for publication in this open access journal is 2400 CHF (Swiss Francs). Submitted papers should be well formatted and use good English. Authors may use MDPI's English editing service prior to publication or during author revisions.

Keywords

  • vibrations: theory and application
  • dynamics of mechanisms and machines
  • multi-degrees-of-freedom systems
  • control systems

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Published Papers (2 papers)

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Research

16 pages, 8137 KiB  
Article
On Large Amplitude Vibrations of the Softening Duffing Oscillator at Low Excitation Frequencies—Some Fundamental Considerations
by Utz von Wagner, Lukas Lentz, Hannes Dänschel and Nils Gräbner
Appl. Sci. 2024, 14(23), 11411; https://doi.org/10.3390/app142311411 - 7 Dec 2024
Viewed by 1115
Abstract
The Duffing equation containing a cubic nonlinearity is probably the most popular example of a nonlinear oscillator. For its harmonically excited, slightly damped, and softening version, stationary large amplitude solutions at subcritical excitation frequencies are obtained when standard semi-analytical methods like Harmonic Balance [...] Read more.
The Duffing equation containing a cubic nonlinearity is probably the most popular example of a nonlinear oscillator. For its harmonically excited, slightly damped, and softening version, stationary large amplitude solutions at subcritical excitation frequencies are obtained when standard semi-analytical methods like Harmonic Balance or Perturbation Analysis are applied. These solutions have the shape of a nose in the amplitude-frequency diagram. In prior work, it has been observed that these solutions may contain large errors and that high ansatz orders may be necessary when applying the Harmonic Balance or other semi-analytical methods to make them converge. Some of these solutions are observed to be asymptotically stable, while in most cases, they are unstable. The current paper aims to give a descriptive explanation for this behavior of the nose solutions, which is mainly related to the exact solution of the free undamped vibrations. Based on this, approximations of the nose solutions are calculated with a procedure combining properties of Perturbation Analysis and Harmonic Balance. Therein, the exact solution of the free undamped vibrations is taken as the zeroth approximation, while higher-order solution parts are calculated by balancing the harmonics, and the phase shift of the zeroth approximation is calculated by a residuum minimization. This method just requires the solution of a system of linear algebraic equations, while systems of nonlinear algebraic equations have to be solved in the case of directly applying Harmonic Balance. Full article
(This article belongs to the Special Issue Phenomena in Nonlinear Dynamical Systems: Theory and Application)
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19 pages, 6497 KiB  
Article
Nonlinear Model Predictive Control with Evolutionary Data-Driven Prediction Model and Particle Swarm Optimization Optimizer for an Overhead Crane
by Tom Kusznir and Jarosław Smoczek
Appl. Sci. 2024, 14(12), 5112; https://doi.org/10.3390/app14125112 - 12 Jun 2024
Cited by 1 | Viewed by 1373
Abstract
This paper presents a new approach to the nonlinear model predictive control (NMPC) of an underactuated overhead crane system developed using a data-driven prediction model obtained utilizing the regularized genetic programming-based symbolic regression method. Grammar-guided genetic programming combined with regularized least squares was [...] Read more.
This paper presents a new approach to the nonlinear model predictive control (NMPC) of an underactuated overhead crane system developed using a data-driven prediction model obtained utilizing the regularized genetic programming-based symbolic regression method. Grammar-guided genetic programming combined with regularized least squares was applied to identify a nonlinear autoregressive model with an exogenous input (NARX) prediction model of the crane dynamics from input–output data. The resulting prediction model was implemented in the NMPC scheme, using a particle swarm optimization (PSO) algorithm as a solver to find an optimal sequence of the control actions satisfying multi-objective performance requirements and input constraints. The feasibility and performance of the controller were experimentally verified using a laboratory crane actuated by AC motors and compared with a discrete-time feedback controller developed using the pole placement technique. A series of experiments proved the effectiveness of the controller in terms of robustness against operating condition variation and external disturbances. Full article
(This article belongs to the Special Issue Phenomena in Nonlinear Dynamical Systems: Theory and Application)
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